This verifies (REF ) and further verifies Lindeberg's condition.
Thus, the central limit theorem of martingale in [1]} leads to (b).
For (c), we apply [2]} with \(\epsilon = \sqrt{\varphi _t}\) , \(\delta = 0\) , \(\rho =1\)  (in their notation), as proved for verifying Lindeberg's condition above, and obtain the normalized result immediately.
This completes the proof.
